A.5.7: Section 5.7 Answers
- Page ID
- 43771
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. \(y_{p}=\frac{-\cos 3x\ln |\sec 3x+\tan 3x|}{9}\)
2. \(y_{p}=-\frac{\sin 2x\ln |\cos 2x|}{4}+\frac{x\cos 2x}{2}\)
3. \(y_{p} = 4e^{x} (1 + e^{x} ) \ln(1 + e^{−x} )\)
4. \(y_{p} = 3e^{x} (\cos x \ln | \cos x| + x \sin x)\)
5. \(y_{p}=\frac{8}{5}x^{7/2}e^{x}\)
6. \(y_{p}=e^{x}\ln (1-e^{-2x})-e^{-x}\ln (e^{2x}-1)\)
7. \(y_{p}=\frac{2(x^{2}-3)}{3}\)
8. \(y_{p}=\frac{e^{2x}}{x}\)
9. \(y_{p}=x^{1/2}e^{x}\ln x\)
10. \(y_{p}=e^{-x(x+2)}\)
11. \(y_{p}=-4x^{5/2}\)
12. \(y_{p} = −2x^{2} \sin x−2x \cos x\)
13. \(y_{p}=-\frac{xe^{-x}(x+1)}{2}\)
14. \(y_{p}=-\frac{\sqrt{x}\cos\sqrt{x}}{2}\)
15. \(y_{p}=\frac{3x^{4}e^{x}}{2}\)
16. \(y_{p}=x^{a+1}\)
17. \(y_{p}=\frac{x^{2}\sin x}{2}\)
18. \(y_{p}=-2x^{2}\)
19. \(y_{p}=-e^{-x}\sin x\)
20. \(y_{p}=-\frac{\sqrt{x}}{2}\)
21. \(y_{p}=\frac{x^{3/2}}{4}\)
22. \(y_{p}=-3x^{2}\)
23. \(y_{p}=\frac{x^{3}e^{x}}{2}\)
24. \(y_{p}=-\frac{4x^{3/2}}{15}\)
25. \(y_{p}=x^{3}e^{x}\)
26. \(y_{p}=xe^{x}\)
27. \(y_{p}=x^{2}\)
28. \(y_{p} = xe^{x} (x − 2)\)
29. \(y_{p}=\sqrt{x}e^{x}(x-1)/4\)
30. \(y=\frac{e^{2x}(3x^{2}-2x+6)}{6}+\frac{xe^{-x}}{3}\)
31. \(y = (x − 1)^{2} \ln(1 − x) + 2x^{2} − 5x + 3\)
32. \(y = (x^{2}−1)e^{x}−5(x−1)\)
33. \(y=\frac{x(x^{2}+6)}{3(x^{2}-1)}\)
34. \(y=-\frac{x^{2}}{2}+x+\frac{1}{2x^{2}}\)
35. \(y=\frac{x^{2}(4x+9)}{6(x+1)}\)
38.
- \(y=k_{0}\cosh x+k_{1}\sinh x+\int _{0}^{x}\sinh (x-t)f(t)dt\)
- \(y'=k_{0}\sinh x+k_{1}\cosh x+\int _{0}^{x}\cosh (x-t)f(t)dt\)
39.
- \(y(x)=k_{0}\cos x+k_{1}\sin x+\int _{0}^{x}\sin (x-t)f(t)dt\)
- \(y'(x)=-k_{0}\sin x+k_{1}\cos x+\int_{0}^{x}\cos (x-t)f(t)dt\)